1. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. If 50 women are randomly selected, find the probability that they have a mean pregnancy between 266 days and 269 days. 2. A car-wash operator counts the number of cars arriving at the premises and finds that, on average, there are 8 per hour. Find the probability that there are at least two cars in the car- wash in any 30-minues period.
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- Assume that, with probability 0.8, It’s going to snow and/or I’m going to stay at home; and with probability 0.7, when it snows, then I stay at home. What is the probability of being truth that I am going to stay at home?Each year a certain amount of money is deposited in an account which pays an annual interest rate of are so that at the end of the year the balance in the account is multiplied by a growth factor of X equals 2+ R. $500 is deposited at the start of the first year, an additional 200 is deposited at the start of the second year, and 600 and start of the following yearAt the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…
- Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ=1/10. If someone arrives immediately ahead of you at a public telephone booth, find the probability that you will have to wait, (a) More than 10 minutes (b) Between 10 and 20 minutesIf the probabilities that a newly manufactured bottle of soap will be free of major defects, free of minor blemishes, and free of major defects and minor blemishes are 0.98, 0.8, and 0.78, respectively, find the probability that a bottle (a) that is free of major defects will also be free of minor blemishes. (b) that is free of minor blemishes will also be free of major defects.1) The mortality rate for a certain disease is 6 per 1000. What is theprobability for just four deaths from that disease in a group of 400?2) Find the probability that at most 5 defective diodes will be found in a pack of 600 diodes if previous data shows that 1% of such diodes are defective.
- Let X = { ⟨Y⟩ | Y is a DFA and for every s in L(Y), ? = ab where a = b}. Show that X is decidable.You wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.We are given that the incubation time is normally distributed with a mean of 35 days and standard deviation of 2 days. Therefore, ? = and ? = .We wish to determine how many of the 10,000 eggs can be expected to hatch in 31 to 39 days. Since 35 − 31 = 4, 31 days is located standard deviations to the left of the mean. Similarly, 39 days is located standard deviations to the right of the mean.
- In a certain city district the need for money to buy drugs is stated as the:reason for 75% of all thefts. Find the probability that among the next 5theft cases reported in this district,a. Exactly 2 resulted from the need for money to buy drugs;b. At most 3 resulled from the need for money to buy drugs.It's a Statistical Machine learning question and not a programming question. 5. Let D be the distribution of training data and D′ be that of test data. A key condition under which classical PAC learning results hold is that D′ = D. Give an example to show that when D′ ̸= D, any learner with access to finite training data, even with unlimited computational power, may incur a high testing error.Suppose that the grading of x University courses is as follows:• Each student can get grades between 0 and 100.• If the student's grade is less than 40, the student is informed that the course failed (Unsuccessful).• If the student's grade is higher than 40,o The difference between the student's current grade and the number that is a multiple of 5 higher than the closest to his / her grade is less than 3.If it is lower, the student's grade is equal to the 5 fold higher than the closest one.o If the difference is 3 or more than 3, no change is made in the grade of the student.In this context, the updated grades of the students are calculated according to the entered student gradesWrite the Java code showing.Solve this question in c ++ language.ü Define the section to be calculated as Java object ("Question1").ü Question1; Take the note string as input.public Question1 (int [] input)ü Print out the updated notes as a series after the calculation is madeo public int [] gradingStudents…